This disclosure explains systems and methods of using phase differences in optical signals to encode data that can be subject to accurate decoding at a receiving end. Earlier technologies for this kind of work include differential phase shift keying protocols that detect changes in phase to transfer a bit of information. Quadrature differential phase shift keying (4-DPSK) is similar but uses one symbol to transfer two bits of information.
The embodiments provided herein address two challenges in optical communication. One is how to increase the photon efficiency or information density on an optical link. The second challenge is how to carry information through turbid media without data degradation.